Polynomial ring: Difference between revisions
New page: Given a (commutative) ring <math>R</math>, the polynomial ring <math>R[x]</math> is, informally, "the ring of all polynomials in <math>x</math> with coefficients in <math>R</math>." |
more formal definition? do we need to prove ringness? also {{stub}} |
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Given a (commutative) [[ring]] <math>R</math>, the polynomial ring <math>R[x]</math> is, informally, "the ring of all polynomials in <math>x</math> with coefficients in <math>R</math>." | Given a (commutative) [[ring]] <math>R</math>, the polynomial ring <math>R[x]</math> is, informally, "the ring of all polynomials in <math>x</math> with coefficients in <math>R</math>." | ||
<cmath>R[x]=\left\lbrace\sum_{i=0}^\infty a_ix^i\mid a_i\in R\right\rbrace</cmath> | |||
<!-- do we need to prove the ringness of R[x]?--> | |||
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Revision as of 10:40, 26 March 2009
Given a (commutative) ring 
, the polynomial ring ![$R[x]$](http://latex.artofproblemsolving.com/1/4/d/14de719c0fff2385124cfbcbd01a2dbb7b9b3300.png)
is, informally, "the ring of all polynomials in 
with coefficients in ."
![\[R[x]=\left\lbrace\sum_{i=0}^\infty a_ix^i\mid a_i\in R\right\rbrace\]](http://latex.artofproblemsolving.com/d/5/8/d585db85a93fbd2eab2e56ca74c12011e2059d6c.png)
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